fractions - the basics

Learning Objective:

• we are learning to use fractions to describe amounts and use pictures to represent fractions.

Investing:

• Most people use fractions almost every day. A simple example is when we talk about taking half of something.
• A real-life use of fractions is sharing cake or pizza. This example is used lots by teachers because their round shape makes it easy to show how they can be divided into equal pieces.
• Understanding fractions is essential before you can become fluent in algebra, makes sense of ratio, decimals and percentages and allows you to do calculations and comparisons in shape, data and almost all other areas of mathematics.
• A 'free gift' with understanding fractions is being able to work with the special fractions called percentages.
• This could help you if you want to work in the modern world! Almost any job this side of subsistence farming uses fractions somewhere even if it is only in calculating tax on your wages.

Preparing:

• To be ready you need only to be able to count to a small number. We assume you can.

Discovering:

• Can you figure it out yourself from these examples?

random fraction picture.xlsm

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• Now try to say the fraction that is shaded blue aloud. Better still write it on a mini-whiteboard and show your teacher:

random fraction picture 2.xlsm

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• Investigate other ways of showing a fraction of an amount.

Modeling:

• Here are some examples of people getting it wrong in typical ways:

The teacher has marked this wrong. Explain why.

This is another common mistake. Explain to this pupil what they've got confused about.

Who is right Ron or Harry? Can you stop them arguing?

• Here are some more examples. Did they get it right or wrong? Explain how you know!

Discussing:

• What would this one be? Tell your learning partner. Convince them you're right.
• Explain how you know.
• How would you explain this to someone who was new to it?

Explaining:

• One way to find the fraction is:
  • check the pieces are the same size. If they aren't, walk away!
  • count the total number of pieces - put this on the bottom of the fraction. It's called the 'denominator.'
  • count the number of pieces shaded - put this number on the top of the fractions. It's the 'numerator.'
• Watch out for pieces that aren't the same size. It is allowed for them to be different shapes, but that's just being nasty. Here's an example:

• A common mistake is... you tell me. You've seen some examples above.
• You can check your result by... go on, explain how you know.

Practicing:

• Some straightforward examples.
• Some harder examples.
• Some mixed examples.
• Some non-examples to spot and some mixed questions with redundant, insufficient or contradictory data.
• You can demonstrate fluency by at least...

Assessing:

• Check you've mastered this skill by having another go at the 'what fraction is shaded blue?' game above.

Developing:

• Next we could learn about fractions that give the same proportion shaded: equivalent fractions.